CN112836422B - Interference and convolution neural network mixed scheme measuring method - Google Patents

Interference and convolution neural network mixed scheme measuring method Download PDF

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CN112836422B
CN112836422B CN202011640018.XA CN202011640018A CN112836422B CN 112836422 B CN112836422 B CN 112836422B CN 202011640018 A CN202011640018 A CN 202011640018A CN 112836422 B CN112836422 B CN 112836422B
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杨元杰
付鑫
董淼
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a measuring method of a mixed scheme of interference and convolution neural networks, and provides a scheme of combining plane wave, vortex light interference and Convolution Neural Networks (CNN) aiming at free space optical communication based on the CNN so as to realize effective identification of multi-path vortex light beams in an atmospheric turbulence environment. The recognition performance of the multi-path vortex light beams under different turbulence levels is researched, and the feasibility and the efficiency of the scheme are verified. In addition, the recognition performance of multiple LG light beams with the same size and opposite signs under different turbulence levels is researched, and the advantages of the scheme are verified. Simulation shows that under the level of weak to medium turbulence, the topological load of the LG light beam can be directly read by adopting an interference method, so that two thirds of workload can be reduced, and the efficiency is greatly improved.

Description

Interference and convolution neural network mixed scheme measuring method
Technical Field
The application relates to a method for measuring a mixed scheme of an interference and convolution neural network, in particular to the field of measurement of a Laguerre Gaussian beam mixed scheme.
Background
Since Alen et al demonstrated in 1992 that the laguerre gaussian beam has a well-defined orbital angular momentum of lh, (where l is the number of topological charges, h ═ h/2 pi, and h is the planck constant), this has attracted considerable attention by researchers to vortex rotation. Because the dimension of the OAM state is infinite and different OAM modes are mutually orthogonal, the method provides a potential solution for realizing high-capacity optical communication in the future. And because the eddy optical rotation has special spiral phase wave front characteristics, the OAM is transferred from the LG light beam to the trapped particle to rotate the particle, and the new idea is provided for optical micro-operation. In addition, the optical imaging and astronomy fields are widely applied.
Recently, convolutional neural networks have become the main machine learning method for visual object recognition. Aiming at OAM identification, a Convolutional Neural Network (CNN) is applied to OAM optical communication to realize efficient demodulation of LG light beams, an OAM demodulator is trained through an AlexNet model, and meanwhile, compared with a traditional conjugate demodulation method, the accuracy rate of the method is far higher than that of the traditional method. Because the performance of an optical communication system based on OAM is easily affected by atmospheric turbulence, the OAM spectrum is subjected to dispersion, and crosstalk and larger bit errors of data transmission are caused.
Generally, in the above researches, a large number of intensity pictures are collected, then the intensity pictures are sent to a convolutional neural network for training, and finally demodulation is performed. And if the convolutional neural network is deep, a significant amount of time is required for CNN training. Therefore, different from the above work, the work of the inventor can directly and accurately read the numerical value of the topological charge under the medium turbulence and weak turbulence levels by using the intensity diagram collected by the CCD through the atmospheric turbulence transmission after the interference of the plane wave and the vortex light. Then, we use CNN for identification when there is strong turbulence. Through the research on the identification performance under different turbulence levels, the feasibility of the scheme is verified, the topological charge sign is also researched to be opposite, vortex light with the same size is transmitted in a turbulence channel after interfering with plane waves, the scheme has higher identification precision, and a new thought is provided for the topological charge identification of the actual OAM-based communication system.
Disclosure of Invention
An interference and convolution neural network mixed scheme measuring method includes establishing an expression E of vortex light beams according to an angle formed by plane wave front oblique incidence and an x axis1And simplified vortex beam expression E2(ii) a Calculating the light intensity I of the interference field; the method is characterized in that a random phase screen is inserted into a light beam propagation path to simulate a turbulent flow channel, and a power spectrum model:
Figure BDA0002879764800000021
wherein k isx,kyThe wave numbers in the x-direction and the y-direction respectively,
Figure BDA0002879764800000022
(l0inner scale of atmospheric turbulence), L0Is the outer dimension of atmospheric turbulence. Refractive index structure constant
Figure BDA0002879764800000023
Is a measure of the intensity of the refractive index fluctuations.
The power spectral density of the phase is approximately calculated, a beam of Gaussian light is simulated at a transmitting end, then the Gaussian light is irradiated onto a reflective liquid crystal Spatial Light Modulator (SLM) loaded with a hologram, the Gaussian light is modulated into corresponding vortex light, and the LG light beams with different topological loads (such as 1,2,3 and 4K) can be generated by controlling a grating image on the hologram. Then, the incident light is obliquely incident with a plane wave and interferes with the LG beam, and the intensity pattern after interference is split. As the topological load changes, the number of splits also changes. The interfered LG beam is then transmitted in a free-space atmospheric turbulence channel, which is simulated by inserting a random phase screen in the transmission path.
And at a receiving end, acquiring a light intensity image transmitted by the atmospheric turbulence through a CCD (charge coupled device). The key to designing the method is that by observing the light intensity image, the topological charge value of most LG light beams can be directly identified, which corresponds to the weak sum of the turbulence intensity. When the strong turbulence is generated, the light intensity image under the strong turbulence is acquired for training, and the light intensity image under the strong turbulence is acquired.
The intensity map after interference collected under strong turbulence and the intensity map without interference under different turbulence levels are sent to CNN respectively. Each case contained 5000 pictures, 4000 for training and 1000 for testing.
The input single-mode LG light beam is adjusted to be topological load { l ═ 1,2,3,4,5,6,7,8,9 and 10} by the same model and method, and then light intensity images after transmission in a turbulent flow channel under interference and interference-free conditions are respectively collected.
Directly reading out the value of the topological load through the interfered intensity image; the post-interference and non-interference intensity images collected at the high turbulence level are then fed into the CNN.
Drawings
FIG. 1 is a graph of intensity after interference of vortex rotation with a plane wave and the corresponding vortex optical phase;
fig. 2 shows a convolution calculation process, in which a 4 × 4 picture is input to perform convolution calculation with a 2 × 2 convolution kernel, and then a 3 × 3 feature map is generated in a convolution layer;
FIG. 3 is a convolutional neural network structure; scaling the original LG beam intensity image to 100 × 100 at the input layer, 32 98 × 98 feature maps were generated by convolving the input image with a 3 × 3 convolution kernel on convolutional layer 1(Conv 1); then on convolutional layer 2(Conv2), 32 96 × 96 feature maps were generated by convolving the input of the previous layer with a convolution kernel of 3 × 3; then on pooling layer 1(Pool1), 32 48 × 48 feature maps were generated by maximal pooling; repeating the previous convolution pooling operation, and finally fully connecting 256 nodes in the full connection layer 1(FC1) with nodes in the pooling layer 3(Pool3) and then fully connecting 512 nodes in the full connection layer 2(FC 2); finally, the output layer of the network outputs the classification probability of the test image to complete the classification task;
fig. 4 is a schematic diagram based on a plane wave and OAM optical interference scheme;
FIG. 5(a) is weak turbulence and (b) is medium turbulence; (c) is highly turbulent;
FIG. 6 identification accuracy under the vortex light intensity turbulence after interference;
fig. 7 is a graph of intensity across different levels of turbulence for the topological loads, { l ═ 1,2,3,4,5,6,7,8,9,10 }; (a) is weak turbulence, (b) is medium turbulence; (c) is highly turbulent;
Detailed Description
Plane waves interfere with vortex light in two forms, parallel interference and non-parallel interference. The case of non-parallel interference is considered here, and for the sake of calculation, it is assumed that a plane wavefront is obliquely incident at an angle of 45 ° to the x-axis, which is expressed as
E1＝A1exp(ik(x+z))， (1)
The simplified optical field expression of the vortex beam is
Figure BDA0002879764800000031
Wherein E1Is a light field expression, A1,A2Is amplitude, l is E2Z is the transmission distance, x is the distance on the x-axis,
Figure BDA0002879764800000032
is the azimuth, i is the complex number, and k is the wavenumber. The intensity of their interference fields can be expressed as:
Figure BDA0002879764800000041
wherein'. is a complex conjugate. The result shows that after the inclined plane wave interferes with the vortex light beam, the interference field is in a fork-shaped distribution. Because the intensity of the vortex light beam has a circular ring structure, the central light intensity is 0, and the intensity diagram after the actual vortex light beam interferes with the plane wave and the corresponding vortex light phase are as shown in fig. 1.
Atmospheric turbulence model:
light is transmitted in the atmosphere and is absorbed and flashed by atmosphere composition gas and particles, so that the light wave is attenuated; and also by refractive index fluctuations, leading to irradiance fluctuations, beam spread, and the like. These have profound effects on eddy-optically-based communication systems, such as modal crosstalk, helical wavefront phase distortion, dispersion of OAM spectra, and the like. In order to study the effect of atmospheric turbulence on vortex rotation, a turbulence channel is simulated by inserting a random phase screen in a light beam propagation path, and a power spectrum model is as follows:
Figure BDA0002879764800000042
wherein phinIs the power spectral density, Cn 2Is the density of atmospheric turbulence, kx,kyThe wave numbers in the x-direction and the y-direction respectively,
Figure BDA0002879764800000043
(l0inner scale of atmospheric turbulence), L0Is the outer dimension of atmospheric turbulence. Refractive index structure constant
Figure BDA0002879764800000044
Is a measure of the intensity of the refractive index fluctuations. Under the Markovian approximation, the power spectral density of the phase is expressed as:
Φφ(kx,ky)＝2π2k2Δzφn(kx,ky) (5)
wherein the wave number
Figure BDA0002879764800000045
Δ z is the spacing between adjacent phase screens. Next, the phase distribution of the atmospheric turbulence can be obtained using the fast fourier transform according to equations (2) and (1) in a cartesian coordinate system:
Figure BDA0002879764800000046
where FFT represents fast fourier transform, C is a complex gaussian random matrix with mean 0 and variance 1, and N and Δ x are the size of the phase screen and the sampling interval, respectively.
Concept of convolutional neural network:
convolutional neural networks are one of the most widely used neural networks, and are mainly used in the field of image recognition, but have unusual expression in the fields of natural language processing, speech recognition and the like. These all benefit from the advantages of CNN with local connectivity, weight sharing, multi-tier sharing, etc.
Generally, convolutional neural networks compound a plurality of convolutional and pooling layers, and finally realize output at a connection layer. The convolution layer is mainly used for carrying out dimension reduction sampling on sample data through convolution calculation so as to obtain data with spatial correlation. An example of a two-dimensional convolution operation is shown in fig. 2, where a 2 × 2 convolution kernel is convolved with a 4 × 4 input image to obtain a 3 × 3 feature map. Then, the data dimension is warped to obtain more continuous probability density space by performing nonlinearity through a nonlinear function (such as RELU) at the active layer. Next, in between successive convolutional layers is a pooling layer for compressing the dimensionality of the data to reduce overfitting, and typically we choose the largest pooling layer, i.e., take the maximum value to replace the pixel characteristics of a region. So that multiple stages of convolution, non-linearity and pooling are stacked. The convolution and full join phases follow. The fully connected layer and all the neural network layers are connected by weight, and classification is realized by a nonlinear activation function and a softmax classifier. In this context, we have designed an improved CNN structure based on the VGG model, and the detailed structure is shown in fig. 3:
transmission system based on plane wave and OAM optical interference scheme
A schematic diagram of a transmission system in atmospheric turbulence based on a plane wave and LG beam interference scheme is shown in FIG. 4. At the transmitting end, a beam of wavelength lambda 1550nm and beam waist radius omega are simulated0The laser beam is modulated into corresponding vortex light by the Gaussian light which is irradiated to a reflective liquid crystal Spatial Light Modulator (SLM) loaded with a hologram, and the LG light beams with different topological loads (such as l1, 2,3 and 4K) can be generated by controlling a grating image on the hologram. Then, the incident light is obliquely incident with a plane wave and interferes with the LG beam, and the intensity pattern after interference is split. As the topological load changes, the number of splits also changes. The interfered LG beam is then transmitted in a free-space atmospheric turbulence channel, which is simulated by inserting a random phase screen in the transmission path. In the simulation, our parameter settings were as follows: l is0＝50m，l00.0003m, 512N, 200 Δ z. And setting the refractive index structure constant therein
Figure BDA0002879764800000051
Comprises the following steps: 1 × e-15，1×e-14And 1 × e-13Respectively corresponding to intensity of atmospheric turbulenceWeak, neutral and strong.
And at a receiving end, acquiring a light intensity image transmitted by the atmospheric turbulence through a CCD (charge coupled device). The key to designing the method is that by observing the light intensity image, the topological charge value of most LG light beams can be directly identified, which corresponds to the weak sum of the turbulence intensity. When the strong turbulence is generated, the light intensity image under the strong turbulence is acquired for training, and the light intensity image under the strong turbulence is acquired.
In our designed system, to compare the reliability of this scheme, we collected with CCDs the intensity images of LG beams with and without interference, { l ═ 1, ± 2, ± 3, ± 4, ± 5} respectively, at a transmission distance z of 1000m at different levels of atmospheric turbulence, which are partially summarized in fig. 5:
it is clear that the phase distortion of the LG light becomes more and more severe as the atmospheric turbulence becomes stronger. From fig. 5(a) and (b), we can directly identify the value of the topological charge from the light intensity map of the LG beam transmitted after interference. Therefore, the interfered LG light can identify the topological charge value 100% in the middle and weak turbulence level after passing through the atmospheric turbulence, but cannot be directly identified in the strong turbulence as shown in FIG. 5 (c).
Next, the intensity maps after interference collected under strong turbulence and the intensity maps without interference at different turbulence levels were fed separately into CNN in our work. Each case contained 5000 pictures, 4000 for training and 1000 for testing. Where we design the CNN parameter settings as follows: epoch is 32, dropout is 0.25, batch _ size is 100, momentum is 0.9; as can be seen from fig. 6, the scheme using interference under strong turbulence also has an identification accuracy of 51.5%.
Besides, in order to show the generality of the method, the same model and method are adopted, the input single-mode LG beam is adjusted to have a topological load { l ═ 1,2,3,4,5,6,7,8,9,10}, and then light intensity images after transmission in a turbulent channel under interference and interference-free conditions are acquired respectively, and the result is shown in fig. 6. In fig. 7(a) (b), we can directly read out the value of the topological charge through the interfered intensity image; then sending the interference and non-interference intensity images collected under the high turbulence level into the CNN, wherein the image 7(c) is a part of high turbulence image, and the recognition accuracy of the interference scheme combined with the CNN is as follows: 62.7 percent; the recognition accuracy of the CNN in the traditional interference-free method is 59.1%. Therefore, under strong turbulence, the accurate OAM identification can be realized by adopting an interference scheme and combining the CNN. Therefore, based on the scheme of combining the interference method and the CNN, the working efficiency is greatly improved on the basis of improving the identification accuracy.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (3)

1. A measuring method of a mixed scheme of interference and convolution neural networks is characterized in that an expression E of vortex light beams is established according to an angle formed by plane wave front oblique incidence and an x axis1And simplified vortex beam expression E2(ii) a Calculating the light intensity I of the interference field; the method is characterized in that a random phase screen is inserted into a light beam propagation path to simulate a turbulent flow channel, and a power spectrum model:
Figure FDA0002879764790000011
wherein k isx,kyThe wave numbers in the x-direction and the y-direction respectively,
Figure FDA0002879764790000012
l0is the internal scale of atmospheric turbulence, L0Is the outer dimension of atmospheric turbulence; refractive index structure constant
Figure FDA0002879764790000013
Is a measure of the intensity of the refractive index fluctuations;
the power spectral density of the phase is calculated approximately, a beam of Gaussian light is simulated at a transmitting end, then the beam of Gaussian light irradiates a reflective liquid crystal Spatial Light Modulator (SLM) loaded with a holographic plate, the Gaussian light is modulated into corresponding vortex light, and the generation of LG light beams with different topological loads can be realized by controlling a grating image on the holographic plate; then, plane waves are obliquely incident and interfere with the LG light beam, and the interfered intensity graph is forked; as the topological load changes, the number of forks also changes; the interfered LG beam is transmitted in a free space atmosphere turbulence channel, and the channel is simulated by inserting a random phase screen in a transmission path;
at a receiving end, acquiring a light intensity image transmitted by atmospheric turbulence through a CCD (charge coupled device); by observing the light intensity image, directly identifying the topological charge value of most of LG light beams, which corresponds to the weak sum and the middle of turbulence intensity; when the strong turbulence exists, the light intensity image under the strong turbulence is only required to be collected for training, and the LG light beam topological charge value under the strong turbulence can not be identified directly by combining with the CNN;
sending the intensity graph after interference acquired under the strong turbulence and the intensity graph without interference under different turbulence levels into CNN respectively; each case contained 5000 pictures, 4000 for training and 1000 for testing;
the input single-mode LG light beam is adjusted to be topological load { l ═ 1,2,3,4,5,6,7,8,9 and 10} by the same model and method, and then light intensity images transmitted in a turbulent flow channel under interference and non-interference conditions are respectively collected;
directly reading out the value of the topological load through the interfered intensity image; the post-interference and non-interference intensity images collected at the high turbulence level are then fed into the CNN.
2. The method of claim 1, wherein the optical field expression of the vortex beam is E1＝A1 exp (ik (x + z)); the simplified optical field expression of the vortex beam is
Figure FDA0002879764790000021
Wherein E1Is a light field expression, A1,A2Is amplitude, l is E2Z is the transmission distance, x is the distance on the x-axis,
Figure FDA0002879764790000022
is the azimuth, i is the complex number, and k is the wavenumber.
3. The method for measuring the mixed solution of the interference and convolution neural network of claim 2, wherein the light intensity of the interference field is expressed as:
Figure FDA0002879764790000023
wherein'. is a complex conjugate.
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